Abstract
We study a hidden Markov process which is the result of a transmission of the binary symmetric Markov source over the memoryless binary symmetric channel. This process has been studied extensively in Information Theory and is often used as a benchmark case for the so-called denoising algorithms. Exploiting the link between this process and the 1D Random Field Ising Model (RFIM), we are able to identify the Gibbs potential of the resulting Hidden Markov process. Moreover, we obtain a stronger bound on the memory decay rate. We conclude with a discussion on implications of our results for the development of denoising algorithms.
Highlights
We study the binary symmetric Markov source over the memoryless binary symmetric channel
We argue that the development of denoising algorithsms, relying on thermodynamic Gibbs ideas can result in a superior performance
If we introduce maps F−1, F1 : R → R, given by
Summary
We study the binary symmetric Markov source over the memoryless binary symmetric channel. (ii) The measure P is Bowen-Gibbs for a continuous potential φ : → R, if there exist constants P ∈ R and C ≥ 1 such that for all ω ∈ and every n ∈ N. n−1 k=0 φ (Sk ω). (iii) The measure P is called an equilibrium state for continuous potential φ : → R, if P attains maximum of the following functional h(P) + φ dP = sup h(P ) + φ dP ,. Example considered in the present paper is rather exceptional since one is able to identify the g-function and the Gibbs potential φ explicitly Another interesting question is the estimate of the decay rate ρ. Let us introduce the following functions: for y ∈ {−1, 1}Z+ , put φ(y) = B(w0(y)), h(y) = cosh(w0(y)) exp −B(w0(y)). Since g(y) z1, we obtain the continued fraction expansion (3.12)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
